Regularly, your brain, during a regular dream, is sorting out your memory. But once you start dreaming lucidly, and you keep it that way for more that 1 minute, what does your brain do? In a regular dream you don't control anything, and part of what you're dreaming comes from what happened that day and from your memory too. but once you perform a lucid dream action that doesn't have anything to do with a recent memory, does your brain still do what it's supposed to do in a regular dream, or something else?

Just speculating, and if I'm getting the question right; if during lucid dreaming the brain functions are to a degree similar to those during the waking state then a first time action during a dream should be treated by the brain in a similar way (as if the action was being done for the first time in waking reality); maybe you would have to figure out how to perform the action, maybe experiment and probably the brain would create a new memory. If the same action was to be repeated in a subsequent dream (or in waking reality, if it's a realistic one) then it should be easier to perform?

Great question! There are very few studies that have examined the brain functions during lucid dreams. I'm interested in the scientific aspect of lucid dreaming and have come across the below information on how the brain works differently during a lucid dream.

“The difference in cognition between the two types of dreaming suggests that lucid dreaming occurs when the frontal parts of the sleeper’s brain — which are normally “off-line” during REM sleep — click back in, bringing back self-consciousness. However, the back parts, which process sensations, are not synced up with the wide awake frontal cortex. So instead of taking in information from the outside world, they remain closed off in the word of the dream, creating a virtual world as convincing as the one outside.” - The Huffington Post – By Rayleigh Ping-Ying Chiang, M.D., Shu-Hui Tsai, Ph.D., Rita Carter (The Huffington Post, 02/05/2014)

“Scientists May Have Found The Part of The Brain That Enables Lucid Dreaming”

“…What they found was that participants who were highly lucid during dreams had larger anterior prefrontal cortexes…”

PREFRONTAL CORTEX – “Many authors have indicated an integral link between a person’s will to live, personality, and the functions of the prefrontal cortex.[2] This brain region has been implicated in planning complex cognitive behavior, personality expression, decision making, and moderating social behavior.[3] The basic activity of this brain region is considered to be orchestration of thoughts and actions in accordance with internal goals.” – Wikipedia

“…The research showed that the brains of people with high and low dream lucidity were different. Subjects with high lucidity had greater gray matter volume in the frontopolar cortex, compared to those with low lucidity. …”

Click here for the article: https://blogs.scientificamerican.com/illusion-chasers/the-neuroscience-of-lucid-dreams/

GREY MATTER – “Grey matter refers to unmyelinated neurons and other cells of the central nervous system. It is present in the brain, brainstem and cerebellum, and present throughout the spinal cord.” – Wikipedia

Lucid Dreaming and Brain Activity

“Recent research into a kind of consciousness within the dream state is beginning to tell us more about the brain”

“…Studies led by neuropsychologists Ursula Voss and Martin Dresler have shown that the brain activity during lucid dreaming bears the core features of REM sleep but is distinct from both non-lucid dreaming and the awake state..” – The Guardian – Vaughan Bell – https://www.theguardian.com/science/2014/apr/27/mysteries-lucid-dreaming-brain-consciousness-research

…We further observed increased activation in bilateral frontopolar areas, which have been related to the processing of internal states, e.g., the evaluation of one’s own thoughts and feelings…

…The strongest increase in activation during lucid compared to non-lucid REM sleep was observed in the precuneus, a brain region that has been implicated in self-referential processing, such as first-person perspective and experience of agency…

…Interestingly, we found activation in the bilateral cuneus and occipitotemporal cortices. These areas are part of the ventral stream of visual processing, which is involved in several aspects of conscious awareness in visual perception. While these activations seem puzzling… they are in line with reports of lucid dreamers stating that lucidity is associated with an exceptional brightness and visual clarity of the dream scenery…